3. Consider the following portion of an electric circuit with three relays. Current will flow from point A to point B if there is at least one closed path when the relays are activated. The relays may malfunction and not close when activated. Suppose that the relays act independently of each other and close properly when activated with a probability of 0.8. (a) Let Ri represent the event that relay i closes properly when activated, i = 1, 2, 3. Using these events, write an expression for the event that current will flow when the relays are activated. (b) What is the probability that current will flow when the relays are activated? (c) Given that current flowed when the relays were activated, what is the probability that relay 1 functioned?
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Let \( R_i \) represent the event that relay \( i \) closes properly when activated, where \( i = 1, 2, 3 \). Show more…
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Consider the following portion of an electric circuit with three relays. Current will flow from point $a$ to point $b$ if there is at least one closed path when the relays are activated. The relays may malfunction and not close when activated. Suppose that the relays act independently of one another and close properly when activated, with a probability of $.9 .$ a. What is the probability that current will flow when the relays are activated? b. Given that current flowed when the relays were activated, what is the probability that relay 1 functioned?
Probability
Two Laws of Probability
10. Consider the portion of an electric circuit with three relays shown to the right. Current will flow from point A to point B if there is at least one closed path when the relays are activated. The relays may malfunction and not close when activated. Suppose that the relays act independently of one another and close properly when activated, with a probability of 0.81. (a) What is the probability that current will flow when the relays are activated? (b) Given that current flowed when the relays were activated, what is the probability that relay 1 functioned?
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